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On the extension and generation of set-valued mappings of bounded variation

V. V. Chistyakov, A. Rychlewicz (2002)

Studia Mathematica

We study set-valued mappings of bounded variation of one real variable. First we prove the existence of an extension of a metric space valued mapping from a subset of the reals to the whole set of reals with preservation of properties of the initial mapping: total variation, Lipschitz constant or absolute continuity. Then we show that a set-valued mapping of bounded variation defined on an arbitrary subset of the reals admits a regular selection of bounded variation. We introduce a notion of generated...

On the fixed points in an ω -limit set

Jack G. Ceder (1992)

Mathematica Bohemica

Let M and K be closed subsets of [0,1] with K a subset of the limit points of M . Necessary and sufficient conditions are found for the existence of a continuous function f : [ 0 , 1 ] [ 0 , 1 ] such that M is an ω -limit set for f and K is the set of fixed points of f in M .

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